Aaa Triangle Calculator - Solve Angles, Sides, Area

An aaa triangle calculator solves a triangle when you know its three interior angles and at least one side length. The "AAA" stands for Angle-Angle-Angle, the case where two triangles with the same three angles are similar. Since A + B + C = 180°, the form takes just A and B plus one side, and the calculator returns C, sides b and c, the area, and the perimeter. It is useful for homework, scale models, and any geometry problem where angles are measured first.

• • Solving geometry homework: Confirm a triangle problem when the teacher has only given you angle measurements and one side.
• • Building a scale model: Recover real-world side lengths from a model whose angles and one known edge you can measure.
• • Surveying and drafting: Translate measured bearings (angles) and one baseline distance into the full triangle dimensions.
• • Checking design angles: Verify that a proposed roof, truss, or ramp has the angles and sides you expect before cutting material.

AAA only fixes the shape of a triangle, not its size. Any two triangles with the same three angles are similar, so their sides are scaled copies of each other. To get real side lengths, you also need one side to anchor the scale. This calculator handles that anchoring for you.

Enter any two angles and one side, and the result panel shows the third angle, the other two sides, the area, and the perimeter. The form validates that the angles sum to 180° and that no angle is zero, so you can trust the numbers it returns.

For the general SSS, SAS, and ASA workflows that complement AAA, the triangle calculator handles all three of the other common congruence cases in one tool.

The calculator takes your two angle inputs (A and B) and one reference side, computes the third angle C, and then applies the Law of Sines to recover the missing sides. Area and perimeter follow directly from those sides.

• A, B, C: The three interior angles in degrees. C is computed from A and B.
• a: Reference side length you enter, opposite angle A. Sets the scale.
• b, c: Sides opposite angles B and C, calculated from the Law of Sines.

The Law of Sines is the only trigonometric identity you need. In any triangle, the diameter of the circumscribed circle sets the constant in a/sin(A) = b/sin(B) = c/sin(C), so knowing one side-angle pair fixes the others.

According to Wikipedia, the Law of Sines states that a/sin(A) = b/sin(B) = c/sin(C) for any triangle, and the same source notes the area can be written as ½·a·b·sin(C).

When you already have two sides and the angle between them, the area of an oblique triangle calculator computes the same area with the ½ab sin(C) formula used here.

These four ideas cover what makes an AAA case different from SSS or SAS, and why a single side length is still required by an aaa triangle calculator.

Understanding these four ideas removes the guesswork from AAA problems. The angle sum rule tells you when your input is impossible, and the Law of Sines tells you exactly what to do with a valid input. Similarity explains why a side is still required, and the ½ab sin(C) area formula turns the result into a usable area number.

If your third angle works out to 90°, the right triangle calculator covers the special Pythagorean relationships that apply to that case.

Follow these steps in order. The result panel updates as you type, so you can also treat it as a scratch pad while you try different angles.

1. 1 Enter angle A: Type the first interior angle in degrees. Use 0 < A < 180, otherwise the form rejects the input.
2. 2 Enter angle B: Type the second interior angle. The third angle C is computed as 180 − A − B.
3. 3 Enter side a: Type the length of the side opposite angle A. This single side fixes the scale of the triangle.
4. 4 Read the third angle: Confirm that the displayed angle C is positive. If it is zero or negative, your A and B do not form a valid triangle.
5. 5 Read sides b and c: These are the lengths of the sides opposite angles B and C, computed with the Law of Sines.
6. 6 Use the area and perimeter: Copy the area for material or finish estimates and the perimeter for trim, fencing, or framing totals.

For a roof truss with angles 30° and 60° at the base and a base rafter of 12 ft, enter A = 30, B = 60, side a = 12. C comes out to 90°. The calculator returns side b = 20.78 ft, side c = 24 ft, area = 124.71 sq ft, and perimeter = 56.78 ft. Use side c as the rafter length and the area to order sheathing.

When the measurement you actually have is a side length plus the angles on either end of it, the triangle length calculator solves the AAS case directly without going through the Law of Sines by hand.

Solving AAA triangles by hand is fast once you know the Law of Sines, but the aaa triangle calculator removes a few classes of error that are easy to make on paper.

• • Catches impossible angle combinations: If A and B do not leave a positive third angle, the calculator flags the error before you waste time on the Law of Sines.
• • Skips the unit conversion step: You enter degrees, the calculator converts to radians internally, and you read the sides back in the same length unit you entered.
• • Computes area and perimeter together: Both outputs come from the same three sides, so you get a consistent answer for material and trim planning in one pass.
• • Works for any AAA triangle, not just right triangles: The Law of Sines applies to all three cases (acute, right, obtuse) without a separate formula path.
• • Useful as a similarity check: When two triangles share the same three angles, the side ratios match exactly. The calculator's side outputs let you verify that.

These benefits matter most when the inputs come from a real measurement rather than a textbook. Surveyors, drafters, and model builders all get angle data first and side data last, so an AAA-first workflow is the natural fit.

If your source data is in gradians or radians instead of degrees, the angle converter lets you convert each angle before entering it here.

Four things change the answer the calculator returns, and the limitations below cover the assumptions behind the Law of Sines itself.

• • AAA information is not enough to recover the absolute size on its own. The calculator needs a reference side a; if you only have angles, the result is a family of similar triangles, not one specific triangle.
• • Floating-point rounding means the computed third angle C may display as 60.00 when the true value is 59.9999. Treat the displayed angle as the exact value when feeding the result into other calculations.
• • The Law of Sines assumes a planar Euclidean triangle. It does not apply to spherical triangles (such as longitude/latitude problems on a globe), where a different set of identities is required.

These factors are why the calculator asks for both angles and a side. A real measurement of a physical triangle almost always gives you one accurate side plus angles, which is exactly the AAA-plus-scale data the tool needs.

According to Wikipedia, infinitely many triangles share the same three interior angles because the angles alone fix the shape but not the size, so a single side is required to determine one specific triangle.

Once you have the three side lengths, the triangle area calculator cross-checks the area with Heron's formula for an independent verification.